Volunteering in animal rescue center

Hello,I'm looking for a good, reliable, not too expensive and genuine non-profit organization/program that would give me the opportunity to volunteer in an animal rescue center in South America. I've done a lot of research and it feels like the more I know the less I'm convinced about where to go and with whom. I thought that people who have actually experienced volunteering abroad would be in the best position to help clearing things out. So here I am.

I'm a 22 y.o. male, biology student. Next year I will be in veterinary school, so I have some kind of gap year this winter and I want to make the most out of it. I want to spend 2-3 months (preferably in South-America since I already know basic Spanish) working with exotic animals, getting some experience and actually doing something helpful. I've already narrowed my choice to rescue centers, even though there were a lot of programs offering wildlife conservation projects I’m not looking into doing diversity surveys, I want to get my hands dirty and work with actual animals. And if my biology/vet background can allow me to help even more, that's even better.

So far I've come across expensive programs like project-abroad and frontier (which is already more affordable), but I've been told that I shouldn't be paying this much to volunteer. I know I could work directly with a center and get there on my own, but since I speak little Spanish and haven't traveled much in my life I feel like paying for an airport pickup and some kind of backup in case of emergency would be a good investment. Plus by booking with a credible organization I can be sure that the so-said center is still up and running and is not some kind of zoo/volunteer trap.

So if you have experienced or know a program/organization or even a good rescue center in South-America, please help me out!